Question

If the following statement is true then write $1$ else write $0$.

$n\left(A\right)=n\left(B\right)\Rightarrow A=B$.

Answer 1

Two sets are equal if the number of elements in both the sets are same.

For any two sets $A$ and $B$, if $n\left(A\right)=n\left(B\right)$ then the number of elements in both the sets are same.
But this does not mean, that the elements of both the sets are same.
So, it is not necessary that $A=B$ if $n\left(A\right)=n\left(B\right)$
Hence, the statement is False.